Solve for $x$ and $y$ using elimination. ${6x+6y = 54}$ ${-5x+3y = -21}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${6x+6y = 54}$ $10x-6y = 42$ Add the top and bottom equations together. $16x = 96$ $\dfrac{16x}{{16}} = \dfrac{96}{{16}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {6x+6y = 54}\thinspace$ to find $y$ ${6}{(6)}{ + 6y = 54}$ $36+6y = 54$ $36{-36} + 6y = 54{-36}$ $6y = 18$ $\dfrac{6y}{{6}} = \dfrac{18}{{6}}$ ${y = 3}$ You can also plug ${x = 6}$ into $\thinspace {-5x+3y = -21}\thinspace$ and get the same answer for $y$ : ${-5}{(6)}{ + 3y = -21}$ ${y = 3}$